Problem: The second and fifth terms of an arithmetic sequence are 17 and 19, respectively. What is the eighth term?
Explanation: Let the first term of the arithmetic sequence be $a$, and let the common difference be $d$.  Then the second term is $a + d = 17$, fifth term is $a + 4d = 19$, and the eighth term is $a + 7d$.  Note that $(a + 4d) - (a + d) = 3d$, and $(a + 7d) - (a + 4d) = 3d$, so the terms $a + d = 17$, $a + 4d = 19$, and $a + 7d$ also form an arithmetic sequence.

If 17 and 19 are consecutive terms in an arithmetic sequence, then the common difference is $19 - 17 = 2$, so the next term must be $19 + 2 = \boxed{21}$.